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@section('title')
    Lab 11, Part 3: Fruitful recursion w/ picture.py patterns
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@section('content')

# Lab 11, Part 3: Fruitful recursion w/ picture.py patterns

In `lab11/part3.py` there are two picture variables already defined for you, `block` and `tri`:

```
# Two provided shapes
block = clockwise270(overlay(wedge('darkred'), flipAcrossHoriz(wedge('darkred'))))
tri = triangles('gray', 'magenta')
```

This is a `block`:
<img src="block.png" style="max-width:300px">

This is a `tri`:
<img src="tri.png" style="max-width:300px">

You'll use these pictures for the tasks in this part of the lab.



## Task 1. Towers
Write a **recursive** function called `tower` that creates a vertical stack of pictures as shown below.

`tower` takes two parameters:

1. a picture
2. the number of pictures in the tower

### Examples

<table>
<tr>
<td>
<code>tower(block, 1)</code>
<img src="tower1.png" style="max-width:300px">
</td>
<td>
<code>tower(block, 2)</code>
<img src="tower2.png" style="max-width:300px">
</td>
</tr>
<tr>
<td>
<code>tower(block, 3)</code>
<img src="tower3.png" style="max-width:300px">
</td>
<td>
<code>tower(block, 4)</code>
<img src="tower4.png" style="max-width:300px">
</td>
</tr>
<tr>
<td>
<code>tower(tri, 1)</code>
<img src="onetri.png" style="max-width:300px">
</td>
<td>
<code>tower(tri, 4)</code>
<img src="pix1b.png" style="max-width:300px">
</td>
</tr>
</table>


### Hints
There are hints in [Helpful Hints and Diagrams](/labs/lab11/hints) (see Table of Contents below), in particular, this [Tower diagram](/content/labs/lab11/hints/pictures-tower.png) may be useful.

Look for a smaller version of the same problem in one level, and try to generalize from there. For example, start by figuring out how you'd draw one level:

<img src="tower1.png" style="max-width:300px">

Also, don't forget about the provided functions in `picture.py` which may be used to accomplish your task:

- `empty( )`
- `clockwise90(p)`
- `overlay(p1, p2)`
- `flipAcrossHoriz(p1)`
- `fourPics(p1, p2, p3, p4)` which produces:

<pre>
-----------
| p1 | p2 |
|    |    |
-----------
| p3 | p4 |
|    |    |
-----------
</pre>



## Task 2. Recursive hillsides
Write a function called `hillside` that will create pictures like those shown below.

Hint: there is only one line of code that differs between the `tower` and `hillside` function.

<table>
<tr>
<td>
<code>hillside(block, 1)</code>
<img src="patt2A.png" style="max-width:300px">
</td>
<td>
<code>hillside(block, 2)</code>:
<img src="patt2B.png" style="max-width:300px">
</td>
</tr>
<tr>
<td>
<code>hillside(block, 3)</code>:
<img src="patt2C.png" style="max-width:300px">
</td>
<td>
<code>hillside(block, 4)</code>:
<img src="patt2D.png" style="max-width:300px">
</td>
</tr>
<tr>
<td>
<code>hillside(tri, 1)</code>:
<img src="onetri.png" style="max-width:300px">
</td>
<td>
<code>hillside(tri, 4)</code>:
<img src="pix2b.png" style="max-width:300px">
</td>
</tr>
</table>

## Task 3. Recursive Mountain (time permitting)

*This task is optional; return to it if you complete Part 4 of today's lab and still have time.*

Write a recursive function called `mountain` that takes a picture parameter and a number, and returns a picture as shown below. This is a mountain scene with some wintry weather. Remember that you have all the `picture.py` methods available to you.

There are hints in [Helpful Hints and Diagrams](/labs/lab11/hints) (see Table of Contents below), in particular, this [Mountain diagram](/content/labs/lab11/hints/pictures-mountain.png) may be useful.

<table>
<tr>
<td>
<code>mountain(block, 1)</code>:
<img src="tower1.png" style="max-width:400px">
</td>
<td>
<code>mountain(block, 2)</code>:
<img src="level2.png" style="max-width:400px">
</td>
</tr>
<tr>
<td>
<code>mountain(block, 3)</code>:
<img src="level3.png" style="max-width:400px">
</td>
<td>
<code>mountain(block, 4)</code>:
<img src="level4.png" style="max-width:400px">
</td>
</tr>
<tr>
<td>
<code>mountain(tri, 2)</code>:
<img src="level2tri.png" style="max-width:400px">
</td>
<td>
<code>mountain(tri, 4)</code>:
<img src="level4tri.png" style="max-width:400px">
</td>
</tr>
</table>
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@include('/labs/lab11/_toc')

@stop